1ZHPEVD(1) LAPACK driver routine (version 3.2) ZHPEVD(1)
2
6 ZHPEVD - computes all the eigenvalues and, optionally, eigenvectors of
7 a complex Hermitian matrix A in packed storage
8
10 SUBROUTINE ZHPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, RWORK,
11 LRWORK, IWORK, LIWORK, INFO )
12 CHARACTER JOBZ, UPLO
14 INTEGER INFO, LDZ, LIWORK, LRWORK, LWORK, N
16 INTEGER IWORK( * )
18 DOUBLE PRECISION RWORK( * ), W( * )
20 COMPLEX*16 AP( * ), WORK( * ), Z( LDZ, * )
22
24 ZHPEVD computes all the eigenvalues and, optionally, eigenvectors of a
25 complex Hermitian matrix A in packed storage. If eigenvectors are
26 desired, it uses a divide and conquer algorithm.
27 The divide and conquer algorithm makes very mild assumptions about
28 floating point arithmetic. It will work on machines with a guard digit
29 in add/subtract, or on those binary machines without guard digits which
30 subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could
31 conceivably fail on hexadecimal or decimal machines without guard dig‐
32 its, but we know of none.
33
35 JOBZ (input) CHARACTER*1
36 = 'N': Compute eigenvalues only;
37 = 'V': Compute eigenvalues and eigenvectors.
38 UPLO (input) CHARACTER*1
40 = 'U': Upper triangle of A is stored;
41 = 'L': Lower triangle of A is stored.
42 N (input) INTEGER
44 The order of the matrix A. N >= 0.
45 AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
47 On entry, the upper or lower triangle of the Hermitian matrix
48 A, packed columnwise in a linear array. The j-th column of A
49 is stored in the array AP as follows: if UPLO = 'U', AP(i +
50 (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i +
51 (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. On exit, AP is over‐
52 written by values generated during the reduction to tridiagonal
53 form. If UPLO = 'U', the diagonal and first superdiagonal of
54 the tridiagonal matrix T overwrite the corresponding elements
55 of A, and if UPLO = 'L', the diagonal and first subdiagonal of
56 T overwrite the corresponding elements of A.
57 W (output) DOUBLE PRECISION array, dimension (N)
59 If INFO = 0, the eigenvalues in ascending order.
60 Z (output) COMPLEX*16 array, dimension (LDZ, N)
62 If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
63 eigenvectors of the matrix A, with the i-th column of Z holding
64 the eigenvector associated with W(i). If JOBZ = 'N', then Z is
65 not referenced.
66 LDZ (input) INTEGER
68 The leading dimension of the array Z. LDZ >= 1, and if JOBZ =
69 'V', LDZ >= max(1,N).
70 WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
72 On exit, if INFO = 0, WORK(1) returns the required LWORK.
73 LWORK (input) INTEGER
75 The dimension of array WORK. If N <= 1, LWORK
76 must be at least 1. If JOBZ = 'N' and N > 1, LWORK must be at
77 least N. If JOBZ = 'V' and N > 1, LWORK must be at least 2*N.
78 If LWORK = -1, then a workspace query is assumed; the routine
79 only calculates the required sizes of the WORK, RWORK and IWORK
80 arrays, returns these values as the first entries of the WORK,
81 RWORK and IWORK arrays, and no error message related to LWORK
82 or LRWORK or LIWORK is issued by XERBLA.
83 RWORK (workspace/output) DOUBLE PRECISION array,
85 dimension (LRWORK) On exit, if INFO = 0, RWORK(1) returns the
86 required LRWORK.
87 LRWORK (input) INTEGER
89 The dimension of array RWORK. If N <= 1, LRWORK
90 must be at least 1. If JOBZ = 'N' and N > 1, LRWORK must be at
91 least N. If JOBZ = 'V' and N > 1, LRWORK must be at least 1 +
92 5*N + 2*N**2. If LRWORK = -1, then a workspace query is
93 assumed; the routine only calculates the required sizes of the
94 WORK, RWORK and IWORK arrays, returns these values as the first
95 entries of the WORK, RWORK and IWORK arrays, and no error mes‐
96 sage related to LWORK or LRWORK or LIWORK is issued by XERBLA.
97 IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
99 On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
100 LIWORK (input) INTEGER
102 The dimension of array IWORK. If JOBZ = 'N' or N <= 1, LIWORK
103 must be at least 1. If JOBZ = 'V' and N > 1, LIWORK must be
104 at least 3 + 5*N. If LIWORK = -1, then a workspace query is
105 assumed; the routine only calculates the required sizes of the
106 WORK, RWORK and IWORK arrays, returns these values as the first
107 entries of the WORK, RWORK and IWORK arrays, and no error mes‐
108 sage related to LWORK or LRWORK or LIWORK is issued by XERBLA.
109 INFO (output) INTEGER
111 = 0: successful exit
112 < 0: if INFO = -i, the i-th argument had an illegal value.
113 > 0: if INFO = i, the algorithm failed to converge; i off-
114 diagonal elements of an intermediate tridiagonal form did not
115 converge to zero.
116 LAPACK driver routine (version 3.N2o)vember 2008 ZHPEVD(1)